From Wikipedia, the free encyclopedia

A center of momentum frame (or zero-momentum
frame, or COM frame) of a system is any inertial frame in
which the center
of massis at rest (has zero velocity). Note that the
center of momentum of a system is not a location, but
rather defines a particular inertial frame (a velocity and a
direction). Thus "center of momentum" already means "center of
momentum frame" and is a short form of this
phrase.

A special case of the center of momentum frame is the
center of mass frame: an inertial frame in which
the center of mass (which is a physical point) is at the origin at
all times. In all COM frames, the center of mass is at rest, but it
may not necessarily be at rest at the origin of the coordinate
system.

Properties

In a center of momentum frame the total linear momentum of the
system is zero. Also, the total energy of the system is the
minimal energy as seen from all possible inertial reference frames. In the COM
frame, the total energy of the system is the "rest energy", and
this quantity (when divided by the factor c2) therefore
gives the rest mass or invariant mass of the system.

Example
problem

An example of the usage of this frame is given below - in a
two-body elastic collision problem. The transformations applied are
to take the velocity of the frame from the velocity of each
particle:

where
is given by:

If we take two particles, one of mass m1 moving at
velocity V1 and a second of mass m2, then we
can apply the following formulae: